Common Core: High School - Algebra

This subject covers the foundational concepts and skills of algebra as outlined in the Common Core standards for high school students.

Expressions and OperationsLinear Equations and InequalitiesFunctions and Their Representations
Systems of EquationsQuadratic Equations and ParabolasExponents and Polynomials
Budgeting and Financial PlanningSports Statistics and PerformanceBuilding and Design
Check Your Work and EstimateBreak Down Problems into Smaller Steps
Expressions and Oper...Linear Equations and...Functions and Their ...Systems of EquationsQuadratic Equations ...Exponents and Polyno...Budgeting and Financ...Sports Statistics an...Building and DesignCheck Your Work and ...Break Down Problems ...
Basic Concepts

Functions and Their Representations

What Is a Function?

A function is a rule that assigns each input exactly one output. Think of it as a machine: you put something in, and you always get a specific result out.

  • Notation: \( f(x) \) means “the function of \( x \)”.

Ways to Show Functions

You can represent functions in different ways:

  • Equation: \( f(x) = 2x + 1 \)
  • Table: Showing input and output pairs.
  • Graph: Plotting points and drawing the line or curve.

Why Are Functions Useful?

Functions help us describe relationships, patterns, and changes in the world.

Real-World Connections

  • Predicting how much money you’ll have after saving a certain amount each week.
  • Figuring out how the temperature changes over time.

Key Features

  • Domain: All possible inputs.
  • Range: All possible outputs.

Examples

  • If \( f(x) = 3x \), then \( f(2) = 6 \)

  • Table: If \( x = 1, 2, 3 \), then \( f(x) = 4, 5, 6 \) if \( f(x) = x + 3 \)

In a Nutshell

Functions relate inputs to outputs, showing how things change together.

Key Terms

Function
A relationship where each input has exactly one output.
Domain
The set of all possible input values for a function.
Range
The set of all possible output values for a function.
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Systems of Equations